Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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            <s xml:id="echoid-s5071" xml:space="preserve">Patet ex iſta æquatione altitudinem jactus duplici titulo deficere ab alti-
              <lb/>
            tudine columnæ prementis a, magis nempe deficit, cum celerius deprimitur,
              <lb/>
            tardiuſve elevatur embolus tum etiam cum orificium E ratione canaliculi D
              <lb/>
            amplitudine creſcit. </s>
            <s xml:id="echoid-s5072" xml:space="preserve">Fuerit v. </s>
            <s xml:id="echoid-s5073" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s5074" xml:space="preserve">amplitudo iſtius orificii æqualis amplitudini
              <lb/>
            tubuli D atque pari celeritate embolus deprimatur eleveturque & </s>
            <s xml:id="echoid-s5075" xml:space="preserve">prodibit
              <lb/>
            x = {1/5} a, ſic ut ad quintam partem tantum aſſurgat vena effluens altitudinis a.</s>
            <s xml:id="echoid-s5076" xml:space="preserve"/>
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            <s xml:id="echoid-s5077" xml:space="preserve">(ε) Diſpendium potentiæ abſolutæ jam hoc modo eruetur, poſito prius
              <lb/>
            nullum laborem in elevandum embolum impendi. </s>
            <s xml:id="echoid-s5078" xml:space="preserve">Sit velocitas quâ embolus
              <lb/>
            deprimitur = v, & </s>
            <s xml:id="echoid-s5079" xml:space="preserve">erit potentia abſoluta tempore unius agitationis integræ im-
              <lb/>
            penſa = a v θ (per paragraphum tertium) quia vero effectus in eo conſi-
              <lb/>
            ſtit, ut effluxus fiat per E durante tempore t ipſaque aqua ad altitudinem
              <lb/>
            {mmθθ/mmθθ + μμ tt} X a elevetur, potuiſſet id antlia ſimplex figuræ quadrageſimæ
              <lb/>
            quintæ efficere, ſi pro potentia premente in illa ſumtus fuiſſet cylindrus aqueus
              <lb/>
            altitudinis {mmθθ/mmθθ + μμtt} X a, atque hæc potentia durante tempore t velocitate
              <lb/>
            {θ/t} v egiſſet; </s>
            <s xml:id="echoid-s5080" xml:space="preserve">unde potentia abſoluta in hâc machina ſimplici, qua nihil de illa
              <lb/>
            perditur, requiſita futura fuiſſet =
              <lb/>
            {mmθθ/mmθθ + μμtt} X a X {θ/t} v X t = {mmθθ/mmθθ + μμtt} X a v θ.
              <lb/>
            </s>
            <s xml:id="echoid-s5081" xml:space="preserve">Eſt igitur tota potentia abſoluta ad partem ejus inutiliter perditam ut a v θ ad
              <lb/>
            a v θ - {mmθθ/mmθθ + μμtt} X a v θ ſeu ut mm θθ + μμtt ad μμtt. </s>
            <s xml:id="echoid-s5082" xml:space="preserve">Igitur ſi in-
              <lb/>
            tegra potentia abſoluta deſignetur per P, erit ejus diſpendium = {μμtt/mmθθ + μμtt} X P.</s>
            <s xml:id="echoid-s5083" xml:space="preserve"/>
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            <s xml:id="echoid-s5084" xml:space="preserve">Neceſſe igitur eſt in hâc præ aliis antliis, ut diabetes amplitudine ad-
              <lb/>
            modum ſuperet orificium E, vel ut multiplex adſit. </s>
            <s xml:id="echoid-s5085" xml:space="preserve">Si enim unicus adeſſet,
              <lb/>
            isque amplitudine orificio E æqualis, ſimulque uniformi velocitate ſurſum de-
              <lb/>
            orſumque agitari ponatur embolus, diſpendium oriretur quatuor quintarum
              <lb/>
            totius partium: </s>
            <s xml:id="echoid-s5086" xml:space="preserve">atque ſi vel duplo amplior fiat, etiamnum perdetur dimi-
              <lb/>
            dium potentiæ abſolutæ.</s>
            <s xml:id="echoid-s5087" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5088" xml:space="preserve">(ς) Denique perſpicuum eſt minorem preſſionem ſuſtinere latera catini
              <lb/>
            G E, quam modioli A A, quippe preſſiones iſtæ ſint ut x ad a, id eſt, </s>
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